Wave Analysis Dashboard for the Irish Weather Buoy Network. All analysis computed via {targets} pipeline.
A rogue wave has Hmax/Hs > 2.0 (ratio of maximum individual wave to significant wave height).
Rows: 10,000
Columns: 22
$ time <dttm> 2019-01-01 00:00:00, 2019-01-01 02:00:00, 2019-0…
$ station_id <chr> "M3", "M5", "M3", "M5", "M3", "M2", "M5", "M5", "…
$ call_sign <chr> "62092", "62094", "62092", "62094", "62092", "620…
$ longitude <dbl> -10.548261, -6.704336, -10.548261, -6.704336, -10…
$ latitude <dbl> 51.21596, 51.69042, 51.21596, 51.69042, 51.21596,…
$ atmospheric_pressure <dbl> 1036.938, 1036.804, 1038.770, 1040.808, 1040.857,…
$ air_temperature <dbl> 9.971, 11.045, 10.210, 12.461, 10.107, 7.627, 11.…
$ dew_point <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 9.3, NA, …
$ wind_direction <dbl> 156, 278, 114, 33, 135, 109, 92, 103, 212, 238, 1…
$ wind_speed <dbl> 3.415, 11.195, 10.389, 6.831, 11.385, 14.610, 11.…
$ gust <dbl> 5.835, 18.405, 13.804, 9.677, 15.227, 17.267, 13.…
$ relative_humidity <dbl> 92.578, 72.266, 92.188, 88.281, 90.625, 66.797, 7…
$ sea_temperature <dbl> 11.348, 10.928, 11.074, 10.986, 11.143, NA, 11.07…
$ salinity <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
$ wave_height <dbl> 2.500, 1.719, 2.344, 1.563, 2.188, NA, 1.250, 1.4…
$ wave_period <dbl> 7.969, 6.797, 7.852, 7.969, 7.500, NA, 6.211, 5.0…
$ mean_wave_direction <dbl> 255, 239, 243, 233, 284, NA, 236, 156, 139, NA, N…
$ hmax <dbl> 4.219, 2.578, 3.750, 2.109, 3.516, NA, 1.875, 1.6…
$ tp <dbl> 11.250, 12.070, 11.953, 11.719, 12.539, 3.750, 10…
$ thtp <dbl> 260.156, 237.656, 253.125, 229.219, 322.031, 59.0…
$ sprtp <dbl> 29.531, 21.094, 33.750, 25.313, 39.375, 26.719, 1…
$ qc_flag <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…| Metric | Value |
|---|---|
| Rogue Wave Events | 1603 |
| Stations Analyzed | 5 |
| Max Rogue Ratio | 6.85 |
| Max Hmax Observed | 29.9 m |
| Dataset Start | 2019-02-04 07:00 UTC |
| Dataset End | 2026-02-05 13:00 UTC |
| Days in Dataset | 2558 |
Use the range slider at the bottom to zoom all panels to a specific time period.
rogue_ratio = Hmax/Hs (wave). Values > 2.0 define a rogue wave event. gust_ratio = Gust/Wind (wind). Values > 1.5 indicate a rogue gust.
A rogue gust has Gust/Wind > 1.5 (ratio of peak gust to sustained wind speed). This parallels the rogue wave definition (Hmax/Hs > 2.0).
Use the range slider at the bottom to zoom all panels to a specific time period.
gust_ratio = Gust/Wind. Values > 1.5 define a rogue gust event.
Comparing wave rogue events (Hmax/Hs > 2.0) with gust rogue events (Gust/Wind > 1.5).
| Term | Definition | Reference |
|---|---|---|
| Hs = H1/3 = 4σ | All three mean the same: significant wave height = mean of highest 1/3 of waves = 4 × standard deviation of sea surface | Longuet-Higgins 1952 |
| Hmax | Maximum individual wave height in 17.5-min measurement period | Typically Hmax/Hs ~ 1.5-1.9 |
| Rogue Wave | Wave where Hmax/Hs > 2.0 | Dysthe 2008 |
| Rogue Ratio | = Hmax/Hs. Values > 2.0 indicate a rogue wave | Used in Rogue Waves |
| Gust Ratio | = Peak Gust / Sustained Wind. Typical value ~1.3 | Used in Rogue Gusts |
| Rogue Gust | Observation where Gust/Wind > 1.5 | Used in Rogue Gusts |
| GEV | Generalized Extreme Value distribution for annual maxima | Used in Annual Max Model |
| GPD | Generalized Pareto Distribution for peaks over threshold | Used in Annual Max Prediction |
| Return Level | Value expected to be exceeded once per T years | Used in Annual Max Model |
These three notations all mean the same thing:
- Hs = Significant wave height (common abbreviation)
- H1/3 = Mean of highest 1/3 of waves (original definition)
- 4σ = 4 × standard deviation of sea surface elevation
The equivalence arises from the Rayleigh distribution of wave heights. For a narrow-banded wave spectrum, the theoretical relationship is Hs = 4 × sqrt(m0) where m0 is the variance of sea elevation.
- Statistical requirement: Need ~100+ waves for valid H1/3
- Wave periods typically 5-15 seconds → 17.5 min gives ~70-200 waves
- WMO recommends 20-30 minutes; 17.5 is the practical lower bound
- Trade-off: longer = better statistics, shorter = more temporal resolution
The Generalized Pareto Distribution (GPD) with Peaks Over Threshold (POT) approach fits extremes per station using all exceedances above a high threshold (90%, 95%, or 99% quantile).
Advantages over pooled GEV: - Uses many more data points (all exceedances, not just annual maxima) - Station-specific return levels - Multiple threshold sensitivity analysis
The Generalized Pareto Distribution has CDF for exceedances \(y = x - u\) above threshold \(u\):
\[F(y) = 1 - \left(1 + \frac{\xi y}{\sigma}\right)^{-1/\xi}\]with two parameters:
| Parameter | Symbol | Interpretation |
|---|---|---|
| Scale | \(\sigma\) | Spread of exceedances |
| Shape | \(\xi\) | Tail behaviour (same as GEV) |
Return levels for T-year event:
\[z_T = u + \frac{\sigma}{\xi}\left[(n_y \lambda T)^\xi - 1\right]\]where \(n_y\) = observations per year, \(\lambda\) = exceedance rate.
GPD results depend on threshold choice. Lower thresholds give more data but may violate asymptotic theory. The mev package provides diagnostics.
The pooled GEV analysis below is illustrative only due to only 8 annual maxima. The GPD per-station approach (Tab 1) is preferred.
Spatial dependence modelling: The SpatialExtremes package provides max-stable process models that account for joint extremes across stations.
Bayesian approaches: The mev package supports profile likelihood and Bayesian methods for improved uncertainty quantification.
Storm propagation: Cross-correlation lag analysis between stations could enable offshore-to-nearshore prediction with lead times.
Gust Factor = Peak Gust / Sustained Wind. Typical value ~1.3. Rogue Gust threshold: GF > 1.5 (see Rogue Gusts page for detailed analysis).
| Term | Definition | Used In |
|---|---|---|
| Hs = H1/3 = 4σ | Significant wave height = mean of highest 1/3 = 4×std dev | Definitions |
| Hmax | Max individual wave in 17.5-min period | Rogue Waves |
| Rogue Wave | Hmax/Hs > 2.0 | Rogue Waves |
| Rogue Gust | Gust/Wind > 1.5 | Rogue Gusts |
| Gust Factor | Peak Gust / Sustained Wind (~1.3 typical) | Gust Factor |
| STL | Seasonal-Trend decomposition (Loess) | Trends |
| Method | Description | Used In |
|---|---|---|
| GEV | Block maxima (annual max, n=8) | Annual Max Model |
| GPD | Peaks over threshold (all exceedances) | Annual Max Prediction |
| Return Level | Value exceeded once per T years | Both EVA pages |
| Beaufort | Description | Wind Speed (m/s) |
|---|---|---|
| 0-5 | Calm to Fresh Breeze | 0 - 10.7 |
| 6-7 | Strong Breeze to Near Gale | 10.8 - 17.1 |
| 8-9 | Gale to Severe Gale | 17.2 - 24.4 |
| 10 | Storm | 24.5 - 28.4 |
| 11 | Violent Storm | 28.5 - 32.6 |
| 12 | Hurricane Force | > 32.7 |
- Longuet-Higgins, M.S. (1952). Statistical distribution of sea waves. J. Marine Research, 11, 245-266.
- Dysthe, K. et al. (2008). Oceanic rogue waves. Ann. Rev. Fluid Mech., 40, 287-310.
- Coles, S. (2001). Statistical Modeling of Extreme Values. Springer.
Analysis generated 2026-02-07 21:18 UTC using irishbuoys v0.1.0